Question

In the figure below, B is the center of the circle. NL= 28, OS = 4x-2, RB = 22 and SB = 22. Find the value of x.

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Answer 1

Answer: x = 9

Step-by-step explanation:

RB and SB are 22 units. Since they are both equal, this means the chords NL and OQ are the same length. This is true whenever the chords are the same distance away from the center.

NL = 28, so OQ = 28 as well.

Furthermore, the radius BP cuts chord OQ in half (because BP is perpendicular to OS), which means OS = 28/2 = 14. We are also told that OS = 4x-22

Therefore,

4x-22 = 14

4x = 14+22

4x = 36

x = 36/4

x = 9